uva678

maksyuki 发表于 oj 分类，标签:
12 9月 2015
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A number of K balls are dropped one by one from the root of a fully binary tree structure FBT. Each time the ball being dropped first visits a non-terminal node. It then keeps moving down, either follows the path of the left subtree, or follows the path of the right subtree, until it stops at one of the leaf nodes of FBT. To determine a ball's moving direction a flag is set up in every non-terminal node with two values, eitherfalse or true. Initially, all of the flags are false. When visiting a non-terminal node if the flag's current value at this node is false, then the ball will first switch this flag's value, i.e., from the falseto the true, and then follow the left subtree of this node to keep moving down. Otherwise, it will also switch this flag's value, i.e., from the true to the false, but will follow the right subtree of this node to keep moving down. Furthermore, all nodes of FBT are sequentially numbered, starting at 1 with nodes on depth 1, and then those on depth 2, and so on. Nodes on any depth are numbered from left to right.
For example, Fig. 1 represents a fully binary tree of maximum depth 4 with the node numbers 1, 2, 3, ..., 15. Since all of the flags are initially set to be false, the first ball being dropped will switch flag's values at node 1, node 2, and node 4 before it finally stops at position 8. The second ball being dropped will switch flag's values at node 1, node 3, and node 6, and stop at position 12. Obviously, the third ball being dropped will switch flag's values at node 1, node 2, and node 5 before it stops at position 10.
Fig. 1: An example of FBT with the maximum depth 4 and sequential node numbers.
Now consider a number of test cases where two values will be given for each test. The first value is D, the maximum depth of FBT, and the second one is I, the Ith ball being dropped. You may assume the value of Iwill not exceed the total number of leaf nodes for the given FBT.

Please write a program to determine the stop position P for each test case.
For each test cases the range of two parameters D and I is as below:

Input

Contains l+2 lines.

Line 1          I the number of test cases Line 2          test case #1, two decimal numbers that are separatedby one blank ...                            Line k+1 test case #k Line l+1 test case #l Line l+2 -1             a constant -1 representing the end of the input file

Output

Contains l lines.

Line 1          the stop position P for the test case #1 ...             Line k the stop position P for the test case #k ...             Line l the stop position P for the test case #l

Sample Input

54 23 410 12 28 128-1

Sample Output

1275123255

 

题目类型：完全二叉树模拟

算法分析：不能按照题目直接模拟，因为题目所给的数据过大。由于小球下落的方向与到达节点的小球序数是相关的，即对于节点i来说，第偶数个小球掉落在节点i上会往它的右子节点移动，第奇数个小球掉落在节点i上会往它的左子结点移动。所以可以直接模拟最后一个节点的移动情况，判断节点序号是奇数还是偶数，如果是奇数，就向其左子结点移动，反之，则向其右子节点移动；接着判断此时的节点是往哪走的第几个节点。对于偶数，则直接除以2，反之则加1再除以2